# Force of Water against wall or incline plane

for a project, how the physical force is different when a wall of water hits a flat 90 degree wall vs a smooth tear to ramp shaped surface. Say the water is a tsunami and the wall is a concrete building. How would the force if it hitting that wall differ from it hitting a smooth round ramp starting at ground level rising slightly until it goes back down on the other side.

Any help with my idea would be greatly appreciated and any links to topics I have not been able to find would be amazing (Scholarly Journals, etc.) Something with Concrete (he he) proof such as math equations would be perfect!

Thanks, Ian Small

Let the tsunami be a rectangle $(a,b)$ and let the wall angle be $\alpha$. The momentum of a layer of height $dy$ is $p=\rho a v\ dy$. After $dt$ the lose in momentum just comes from the lose of water since we consider the center of mass to have the same velocity, so $$dp=\rho \tan[\alpha] (v dt)^2v /2$$ where we used $dx=vdt$ and $dy=\tan \alpha vdt$. Since we have to consider the contribution of all the layers $$F=\int dF dy= \rho \tan[\alpha] v ^3 b dt /2$$